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A magnet system for a 28 GHz electron cyclotron resonance ion source is being developed by the Korea Basic Science Institute. The configuration of the magnet system consists of 3 solenoid coils for a mirror magnetic field and 6 racetrack coils for a hexapole magnetic field. They can generate axial magnetic fields of 3.6 T at the beam injection part and 2.2 T at the extraction part. A radial magnetic field of 2.1 T is achievable at the plasma chamber wall. A step type winding process was employed in fabricating the hexapole coil. The winding technique was confirmed through repeated cooling tests. Superconducting magnets and a cryostat system are currently being manufactured.